Orthopairian Entropy and its Application in Preparation and Evaluation of Carrot and Apple Blended Jam with Multicriteria Decision Making

Orthopairian Entropy and its Application in Preparation and Evaluation of Carrot and Apple Blended Jam with Multicriteria Decision Making | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Orthopairian Entropy and its Application in Preparation and Evaluation of Carrot and Apple Blended Jam with Multicriteria Decision Making Zahid Hussain, Ali Haider, Razia Sharif, Rashid Hussain This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3961057/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Yager recognized the broadly generalized q-Rung Orthopair Fuzzy Sets (q-ROFSs) in 2017. This high-class model evaluates uncertainty and vagueness more accurately than Intuitionistic Fuzzy Sets (IFSs) represented by Atanassov in 1986 and Pythagorean Fuzzy Sets (PFSs) developed by Yager in 2014 respectively. We can continually change the value of ‘q’ for determining the facts, so q-ROFSs are reliable and more desirable for the uncertain environment. This theory was clearly formulated to show the ambiguity and uncertain situations mathematically and developed some tools to tackle imprecise information in real-world applications. It has various applications in different fields including fuzzy systems, control system, image processing, data mining and clustering, classification and pattern recognition, control systems, bioinformatics and decision making due to its ability to quantify the uncertainty in a system. The notion of entropy and sigma entropy is commonly used in the field of information theory to quantify the amount of uncertainty or randomness present in a given system. Here, we suggest a novel entropy measure on q-Rung Orthopair Fuzzy Set (q-ROFS) and then extend it to introduce the concept of sigma entropy to measure the fuzziness present in a system under consideration. Also, the suggested entropy measure is axiomatically defined on q-ROFS. We give the proof of every axiom in detail. Furthermore, we put forward some numerical examples with comparisons and analysis to determine the suitability, reliability and consistency of the suggested method. Finally, we develop O-COPRAS (Orthopairian Complex Proportional Assessment) based on proposed entropy measure. To show the practical capability, we apply proposed O-COPRAS for preparing and evaluating blended Jams and ranking for the most economically affected countries in the world by COVID-19 pandemic respectively. Mathematics Subjects Classification 03E72 · 94D05 · 94A17 · 68T10 · 62H30 q-Rung Orthopair Fuzzy Sets Entropy Measures Multicriteria Decision Making Full Text Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3961057","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":505196916,"identity":"b6171e04-5030-46dc-b89b-7d5dc51db7a0","order_by":0,"name":"Zahid Hussain","email":"","orcid":"https://orcid.org/0000-0002-6101-6685","institution":"Karakoram International University","correspondingAuthor":false,"prefix":"","firstName":"Zahid","middleName":"","lastName":"Hussain","suffix":""},{"id":505196917,"identity":"ef5fe78f-a48b-4499-a179-0d0a08320e90","order_by":1,"name":"Ali Haider","email":"","orcid":"","institution":"Karakoram International University","correspondingAuthor":false,"prefix":"","firstName":"Ali","middleName":"","lastName":"Haider","suffix":""},{"id":505196918,"identity":"603fc7ef-1f65-4018-94f1-49cf926e14c9","order_by":2,"name":"Razia Sharif","email":"","orcid":"","institution":"Karakoram International University","correspondingAuthor":false,"prefix":"","firstName":"Razia","middleName":"","lastName":"Sharif","suffix":""},{"id":505196919,"identity":"94b8ec5e-f597-45c4-8ff7-dba4aa55f5a3","order_by":3,"name":"Rashid Hussain","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIie3PsQrCMBCA4SuBc6ntmoLoK7QU6qL4Klc6uDh31Skugqu+heALCIIu0rlji1AXNxdHE4ogDqluIvnJcIF8JAEwmX4zBEIAh7E9kNrvAKzZJwQZJl+QetlhvW8i/fmxKooUetiyb34poOvkhOVKQzqnSd+nDALB2luKBYReTq1goyEcJsjlSUuRnRzijbzFK3TEvVSKjASzz4pMmwmnSJFYEqYeRr4i2ofxa8Qp44lgGMpP8WB9KueB7vvcHVfePR0Ml+7+rIaec0wO5UJDnvJ1sEQzeA+/JyaTyfTPPQDIvEY7wovm1wAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-3260-7280","institution":"Karakoram International University","correspondingAuthor":true,"prefix":"","firstName":"Rashid","middleName":"","lastName":"Hussain","suffix":""}],"badges":[],"createdAt":"2024-02-16 11:28:56","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3961057/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3961057/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91149264,"identity":"24515c18-2ba4-47be-ad25-bfd9da5fc7ee","added_by":"auto","created_at":"2025-09-12 06:48:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":572030,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3961057/v1_covered_b3de0fdb-e607-4425-b5d8-0863ce586d68.pdf"}],"financialInterests":"","formattedTitle":"Orthopairian Entropy and its Application in Preparation and Evaluation of Carrot and Apple Blended Jam with Multicriteria Decision Making","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"q-Rung Orthopair Fuzzy Sets, Entropy Measures, Multicriteria Decision Making","lastPublishedDoi":"10.21203/rs.3.rs-3961057/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3961057/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eYager recognized the broadly generalized q-Rung Orthopair Fuzzy Sets (q-ROFSs) in 2017. 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